New special education teachers often struggle to teach children the mathematics vocabulary necessary to understand and effectively solve math word problems. The authors designed and implemented a pilot program to prepare pre-service teachers majoring in special education to implement the Camelot Learning Math Intervention Program (CLMIP). We met…

This study investigated Spanish-speaking kindergarten students' participation in mathematical discourse as they solved and discussed a range of word problems. Specifically, we draw upon sociocultural perspectives on mathematics learning to frame mathematical discourse and to examine specific teacher and student actions that seemed to support the…

This study compared the effects of delivering a supplemental, small-group tutoring intervention on the mathematics outcomes of third-grade students at risk for mathematics difficulties (MD) who were randomly assigned to either a schema-based instruction (SBI) or control group. SBI emphasized the underlying mathematical structure of additive…

"Welcome to Conversions Rock" is a new math program designed to build and reinforce the important skills of converting fractions, decimals, and percents for students in grades 6-8. Developed by The Actuarial Foundation, this program seeks to provide skill-building, real-world math to help students become successful in the classroom and beyond. [A…

Middle school students struggle to solve mathematical word problems and mathematics teachers require researched based strategies to use when instructing students. Drawing a picture or representation is a strategy that students frequently use, and the purpose of this study was to examine the effects that learner-generated drawing has on a student's…

What is the relationship between addition and subtraction? How do individuals know whether an algorithm will always work? Can they explain why order matters in subtraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by…

This paper presents our initial work to develop trajectories of preservice teachers' knowledge of teaching algebra for equity. We have developed two overlapping hypothetical learning trajectories (HLTs) for teachers' learning to engage and motivate diverse students to solve algebra problems. These HLTs are being used to guide the development of…

Being told procedures and concepts before problem solving can inadvertently undermine the learning of deep structures in physics. If students do not learn the underlying structure of physical phenomena, they will exhibit poor transfer. Two studies on teaching physics to adolescents compared the effects of "telling" students before and after…

This study examines the relationship between the grasp of consciousness of the reasoning process in Grades 5 and 8 pupils from a public and a private school, and their performance in mathematical problems of Cartesian product. Forty-two participants aged from 10 to 16 solved four problems in writing and explained their solution procedures by…

This study investigated the effectiveness of "Math Explorer" at enhancing the word problem-solving skills of students with mathematics difficulties (MD). The study, which had a multiple-probe-across-subjects design, was conducted over 18 weeks. Four students with MD in Grades 2 and 3 participated. All students were able to use the four-step…

In this paper we compare how three teachers, one from each of Finland, Flanders and Hungary, introduce linear equations to grade 8 students. Five successive lessons were videotaped and analysed qualitatively to determine how teachers, each of whom was defined against local criteria as effective, addressed various literature-derived…

Although the characteristics of PBL (problem focused, student centered, self-directed, etc.) are well known, the components of a problem-based learning environment (PBLE) and the cognitive scaffolds necessary to support learning to solve different kinds of problems with different learners is less clear. This paper identifies the different…

Upper primary school children often routinely apply proportional methods to missing-value problems, even when it is inappropriate. We tested whether this tendency could be weakened if children were not required to produce computational answers to such problems. A total of 75 sixth graders were asked to classify 9 word problems of three types (3…

Against the background of concerns around teaching and learning outcomes in primary school mathematics in South Africa, this article presents two studies conducted in American Samoa and seeks to draw implications for the teaching and learning of mathematics in South Africa. American Samoa has a very similar educational context to South Africa. The…

This study compared the effectiveness of computer-mediated instruction (CMI) and teacher-mediated instruction (TMI) on the word problem-solving performance of students struggling in mathematics. Both conditions integrated cognitive modeling that focused on the problem structure using visual representations with critical instructional elements…